| In this thesis we investigate the effect of cabling on the Heegaard Floer homology invariants for knots. We study the homology groups HFK&d14; (S3, K2, n), where K2,n denotes the (2,n) cable of an arbitrary knot, K. The main theorem states that for sufficiently large |n |, the Floer homology of the cabled knot depends only on the filtered chain homotopy type of CFK&d14; (K). In fact, the homology groups in the top 2 filtration dimensions for the cabled knot are isomorphic to the original knot's Floer homology group in the top filtration dimension. The results are extended to (p,pn +/- 1) cables. A corollary of the proof of the theorems shows that if K satisfies g( K) = tau(K), then tau(K 2,2n + 1) = 2tau(K ) + n for all n (where tau is the Ozsvath-Szabo concordance invariant). We apply the theorems to compute HFK&d14; ((T2,2m + 1) 2,2n + 1) for all sufficiently large |n|, where T2,2 m + 1 denotes the (2, 2m + 1)-torus knot. Using other techniques we compute the Floer homology of all (2, n) cables of the trefoil knot. |
